Mesh 3D elements from a fixed 2D mesh

Mesh 3D elements from a fixed 2D mesh

Suppose I have an element consisting of two cubes. One of the cube I want to mesh with hexahedron elements and the other cube with tetrahedron elements between the cubes . The face between the two cubes will have nodes that both builds up a structured mesh of quadrates - which I want to build the hexahedron mesh out of - and of split quadrates/triangles - that the tetrahedron mesh will be built by. So I first want to create the surface mesh (which is no problem) and I then want to create the two volume mesh with this surface mesh hold fix as a condition for the two mesh. Is their any way I can do this?
I know how to create two different mesh at the same time with local hypotheses but I'm interested in how I can hold one surface fixed and create a mesh out of this.
Thank you for any answers on this problem.
/Jonas